Unique solvability of a linear problem with perturbed periodic boundary values

Title:

Unique solvability of a linear problem with perturbed periodic boundary values

Creator:

Mehri, Bahman and Nojumi, Mohammad H.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8f3adc87-d24e-478d-9827-8119085b8998
uuid:8f3adc87-d24e-478d-9827-8119085b8998

Subject:

ordinary differential equations, integral equations, and periodic boundary value problems

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We investigate the problem with perturbed periodic boundary values \[ \left\rbrace \begin{array}{ll}y^{\prime \prime \prime }(x) + a_2(x) y^{\prime \prime }(x) + a_1(x) y^{\prime }(x) + a_0(x) y(x) = f(x) , y^{(i)}(T) = c y^{(i)}(0), \ i = 0, 1, 2; \ 0 < c < 1 \end{array}\right.\] with $a_2, a_1, a_0 \in C[0,T]$ for some arbitrary positive real number $T$, by transforming the problem into an integral equation with the aid of a piecewise polynomial and utilizing the Fredholm alternative theorem to obtain a condition on the uniform norms of the coefficients $a_2$, $a_1$ and $a_0$ which guarantees unique solvability of the problem. Besides having theoretical value, this problem has also important applications since decay is a phenomenon that all physical signals and quantities (amplitude, velocity, acceleration, curvature, etc.) experience.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

351-362

Source:

Czechoslovak Mathematical Journal | 1999 Volume:49 | Number:2

Harvested from:

CDK

Metadata only:

false